Complex Conjugates and Dividing Complex Numbers

Complex Conjugates

Every complex number has a complex conjugate. The complex conjugate of
a + bi
is
a - bi
. For example, the conjugate of
3 + 15i
is
3 - 15i
, and
the conjugate of
5 - 6i
is
5 + 6i
.

When two complex conjugates
a + bi
and
a - bi
are added, the result is
2a
.
When two complex conjugates are subtracted, the result if
2bi
. When two
complex conjugates are multiplied, the result, as seen in
Complex Numbers, is
a2 + b2
.

Dividing Complex Numbers

To find the quotient of two complex numbers, write the quotient as a fraction.
Then multiply the numerator and the denominator by the conjugate of the
denominator. Finally, simplify the expression: